Conditional regularity of very weak solutions to the Navier-Stokes-Fourier system

0460241 - MÚ 2017 RIV US eng C - Conference Paper (international conference)
Feireisl, Eduard - Sun, Y.
Conditional regularity of very weak solutions to the Navier-Stokes-Fourier system.
Recent Advances in Partial Differential Equations and Applications. Providence: American Mathematical Society, 2016 - (Rădulescu, V.; Sequeira, A.; Solonikov, V.), s. 179-199. Contemporary Mathematics, 666. ISBN 978-1-4704-3471-7.
[International Conference on Recent Advances in PDEs and Applications, in honor of Hugo Beirão da Veiga's 70th birthday. Levico Terme (IT), 17.02.2014-21.02.2014]
EU Projects: European Commission(XE) 320078 - MATHEF
Institutional support: RVO:67985840
Keywords : Navier-Stokes-Fourier system * conditional regularity * relative entropy
Subject RIV: BA - General Mathematics
http://www.ams.org/books/conm/666/

We consider a class of (very) weak solutions to the Navier-Stokes-Fourier system describing the time evolution of the density, the absolute temperature, and the macroscopic velocity. It is shown that a weak solution emanating from smooth initial data is regular as long as all the unknowns are bounded and the velocity divergence integrable in the existence interval (0,T). Using the method of relative energy we first show that any weak solution enjoying the above mentioned regularity coincides with a strong one as long as the latter exists. In such a way, the proof reduces to showing that the life span of the strong solution can be extended to the desired existence interval (0,T).
Permanent Link: http://hdl.handle.net/11104/0260370